The transverse shear stiffness of a newly-developed all-metal sandwich core structure is determined experimentally and numerically. The core structure is composed of a periodic array of domes which are introduced into an initially flat sheet through stamping. A finite element model of the stamping process is built and validated experimentally. A parametric study is performed to choose the stamping tool geometry such that the resulting core structure provides maximum shear stiffness for a given relative density. It is found that the optimal geometries for relative densities ranging from 0.2 to 0.35 all feature the same dome shape with the same height-to-width ratio. The simulation results also show that the estimated transverse shear strength of the proposed core structure is the same as that of hexagonal honeycombs of the same weight for high relative densities (greater than 0.35), but up to 30% smaller for low relative densities (lower than 0.2). In addition to numerical simulations of a representative unit cell, four-point bending experiments are performed on brazed prototype sandwich beams to validate the computational model.